The Poisson distribution:
It is used to describe a number of managerial situations including the arrivals of raw material trucks to plant. They can all be described by a discrete random variable that takes on non-negative integer (whole number) values 0, 1, 2, 3, 4, 5 and so on; the number of trucks, arrive at plant in a given interval of time will be 0, 1, 2, 3, 4, and 5 and so on.
Characteristics:
Suppose we use the number of trucks arriving at a plant during the busiest part of the day as an illustration of Poisson Probability Distribution Characteristics:
- The average arrival of trucks 15-minute interval can be estimated.
- If we divide the 15-minute interval into smaller intervals of, say, 1 second each, we will see that these statements are true:
- The probability that exactly one truck will arrive per second is a very small number and is constant for every 1-second interval.
- The probability that two or more trucks will arrive within a 1-second interval is so small that we can safely assign it a 0 probability.
- The number of trucks who arrive in a 1-second interval is independent of where that 1- second interval is within the larger 15-minute interval.
- The number of trucks who arrive in any 1-second interval is not dependent on the number of arrivals in any other 1-second interval.
It is acceptable to generalize from these conditions and to apply them to other processes of interest to management. If these processes meet the same conditions, then it is possible to use a Poisson probability distribution to describe them.
Calculating probabilities using Poisson distribution:
The probability of exactly x occurrences in a Poisson distribution is calculated using the relation
